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CENTRE FOR DYNAMIC MACROECONOMIC ANALYSIS
WORKING PAPER SERIES
CDMA07/20
Can macroeconomic variables explain long
term stock market movements?
A comparison of the US and Japan
Peter Macmillan*
University of St Andrews
Andreas Humpe
University of St Andrews
OCTOBER 2007
ABSTRACT
Within the framework of a standard discounted value model we examine
whether a number of macroeconomic variables influence stock prices in the US
and Japan. A cointegration analysis is applied in order to model the long term
relationship between industrial production, the consumer price index, money
supply, long term interest rates and stock prices in the US and Japan. For the
US we find the data are consistent with a single cointegrating vector, where
stock prices are positively related to industrial production and negatively related
to both the consumer price index and a long term interest rate. We also find an
insignificant (although positive) relationship between US stock prices and the
money supply. However, for the Japanese data we find two cointegrating
vectors. We find for one vector that stock prices are influenced positively by
industrial production and negatively by the money supply. For the second
cointegrating vector we find industrial production to be negatively influenced
by the consumer price index and a long term interest rate. These contrasting
results may be due to the slump in the Japanese economy during the 1990s and
consequent liquidity trap.
Keywords: Stock Market Indices, Cointegration, Interest Rates.
JEL Classifications: C22, G12, E44.
School of Economics and Finance, University of St Andrews, St Andrews, UK, KY16 9AL, Tel:
+44(0)1334 462433, Fax: +44(0)1334 462444, e-mail Address: [email protected]
*
CASTLECLIFFE, SCHOOL OF ECONOMICS & FINANCE, UNIVERSITY OF ST ANDREWS, KY16 9AL
TEL: +44 (0)1334 462445 FAX: +44 (0)1334 462444 EMAIL: [email protected]
www.st-andrews.ac.uk/cdma
I. Introduction.
A significant literature now exists which investigates the relationship between stock
market returns and a range of macroeconomic and financial variables, across a number
of different stock markets and over a range of different time horizons. Existing
financial economic theory provides a number of models that provide a framework for
the study of this relationship.
One way of linking macroeconomic variables and stock market returns is
through arbitrage pricing theory (APT) (Ross, 1976), where multiple risk factors can
explain asset returns. While early empirical papers on APT focussed on individual
security returns, it may also be used in an aggregate stock market framework, where a
change in a given macroeconomic variable could be seen as reflecting a change in an
underlying systematic risk factor influencing future returns. Most of the empirical
studies based on APT theory, linking the state of the macro economy to stock market
returns, are characterised by modelling a short run relationship between
macroeconomic variables and the stock price in terms of first differences, assuming
trend stationarity. For a selection of relevant studies see inter alia Fama (1981, 1990),
Fama and French (1989), Schwert (1990), Ferson and Harvey (1991) and Black,
Fraser and MacDonald (1997). In general, these papers found a significant relationship
between stock market returns and changes in macroeconomic variables, such as
industrial production, inflation, interest rates, the yield curve and a risk premium.
An alternative, but not inconsistent, approach is the discounted cash flow or
present value model (PVM) 1 . This model relates the stock price to future expected
cash flows and the future discount rate of these cash flows. Again, all macroeconomic
factors that influence future expected cash flows or the discount rate by which these
cash flows are discounted should have an influence on the stock price. The advantage
of the PVM model is that it can be used to focus on the long run relationship between
2
the stock market and macroeconomic variables. Campbell and Shiller (1988) estimate
the relationship between stock prices, earnings and expected dividends. They find that
a long term moving average of earnings predicts dividends and the ratio of this
earnings variable to current stock price is powerful in predicting stock returns over
several years. They conclude that these facts make stock prices and returns much too
volatile to accord with a simple present value model.
Engle and Granger (1987) and Granger (1986) suggest that the validity of long
term equilibria between variables can be examined using cointegration techniques.
These have been applied to the long run relationship between stock prices and
macroeconomic variables in a number of studies, see inter alia Mukherjee and Naka
(1995), Cheung and Ng (1998), Nasseh and Strauss (2000), McMillan (2001) and
Chaudhuri and Smiles (2004). Nasseh and Strauss (2000), for example, find a
significant long-run relationship between stock prices and domestic and international
economic activity in France, Germany, Italy, Netherlands, Switzerland and the U.K. In
particular they find large positive coefficients for industrial production and the
consumer price index, and smaller but nevertheless positive coefficients on short term
interest rates and business surveys of manufacturing. The only negative coefficients
are found on long term interest rates. Additionally, they find that European stock
markets are highly integrated with that of Germany and also find industrial production,
stock prices and short term rates in Germany positively influence returns on other
European stock markets (namely France, Italy, Netherlands, Switzerland and the UK).
In this paper, we will draw upon theory and existing empirical work as a
motivation to select a number of macroeconomic variables that we might expect to be
strongly related to the real stock price. We then make use of these variables, in a
cointegration model, to compare and contrast the stock markets in the US and Japan.
In contrast to most other studies we explicitly use an extended sample size of most of
3
the last half century, which covers the most severe stock market booms in US and
Japan. While Japans’ hay days have been in the late 1980s, the US stock market boom
occurred during the 1990s and ended in 2000. Japans’ stock market has not yet fully
recovered from a significant decline during the 1990s, and at the time of writing,
trades at around a quarter of the value it saw at its peak in 1989. 2
The aim of this paper is to see whether the same model can explain the US and
Japanese stock market while yielding consistent factor loadings. This might be highly
relevant, for example, to private investors, pension funds and governments, as many
long term investors base their investment in equities on the assumption that corporate
cash flows should grow in line with the economy, given either a constant or slowly
moving discount rate. Thus, the expected return on equities may be linked to future
economic performance. A further concern might be the impact of the Japanese
deflation on real equity returns. In this paper, we make use of the cointegration
methodology, to investigate whether the Japanese stock market has broadly followed
the same equity model that has been found to hold in the US.
In the following section, we briefly outline the simple present value model of
stock price formation and make use of it in order to motivate our discussion of the
macroeconomic variables we include in our empirical analysis. In the third section we
briefly outline the cointegration methodology, in the fourth section we discuss our
results and in the fifth section we offer a summary and some tentative conclusions
based on our results.
II. Data and motivation
In order to motivate our variable selection, a simple PVM may be formulated as
follows:
4
Pt =
Et (d t +1 ) Et ( Pt +1 )
+
1 + Et r
1 + Et r
(1)
Where Et(.) denotes the expectations operator conditional upon on all information
available at time t, Pt is the fair (real) price of the stock at time t, Et(dt+1) is the
expected annual (real) dividend per share at the end of the first year, Et(Pt+1) is the
expected (real) price of the share at the end of the first year and finally Etr is the
expected (constant) market determined (real) discount rate or cost of capital. By noting
that
Et Pt +i =
Et (d t +i +1 ) Et ( Pt +i +1 )
+
,
1 + Et r
1 + Et r
(2)
for i = 1, …., N-1, by substituting (2) into (1) and repeatedly substituting for the
expected future price term we get:
N
Pt = ∑
i =1
Et (d t +i )
(1 + Et r )
i
+
Et ( PN )
(1 + Et r )N
.
(3)
As T → ∞, (3) becomes:
∞
Pt = ∑
i =1
Et (d t +i )
(4)
(1 + Et r )i
Therefore, the share price depends upon the expected stream of dividend payments
and the market discount rate. Hence, any macroeconomic variable that may be thought
5
to influence expected future dividends and/or the discount rate could have a strong
influence on aggregate stock prices. 3
As suggested by Chen, Roll and Ross (1986), the selection of relevant
macroeconomic variables requires judgement and we draw upon both on existing
theory and existing empirical evidence. Theory suggests, and many authors find, that
corporate cash flows are related to a measure of aggregate output such as GDP or
industrial production 4 . We follow, Chen, Roll and Ross (1986), Maysami and Koh
(1998) and Mukherjee and Naka (1995) and make use of industrial production in this
regard.
Unanticipated inflation may directly influence real stock prices (negatively)
through unexpected changes in the price level. Inflation uncertainty may also affect
the discount rate thus reducing the present value of future corporate cash flows.
DeFina (1991) has also argued that rising inflation initially has a negative effect on
corporate income due to immediate rising costs and slowly adjusting output prices,
reducing profits and therefore the share price. Contrary to the experience of the US,
Japan suffered periods of deflation during the late 1990s and early part of the 21st
century, and this may have had some impact on the relationship between inflation and
share prices
The money supply, for example M1, is also likely to influence share prices
through at least three mechanisms: First, changes in the money supply may be related
to unanticipated increases in inflation and future inflation uncertainty and hence
negatively related to the share price; Second, changes in the money supply may
positively influence the share price through its impact on economic activity; Finally,
portfolio theory suggests a positive relationship, since it relates an increase in the
money supply to a portfolio shift from non-interest bearing money to financial assets
6
including equities. For a further discussion on the role of the money supply see Urich
and Wachtel (1981), Rogalski and Vinso (1977) and Chaudhuri and Smiles (2004).
The interest rate directly changes the discount rate in the valuation model and
thus influences current and future values of corporate cash flows. Frequently, authors
have included both a long term interest rate (e.g a 10 year bond yield) and a short term
interest rate (e.g. a 3 month T-bill rate) 5 . We do not use a short term rate as our aim
here is to find a long term relationship between the stock market and interest rate
variables. Changes in the short rate are mainly driven by the business cycle and
monetary policy. In contrast, the long term interest rate should indicate the longer term
view of the economy concerning the discount rate.
For our long term rate using the US data we have chosen a 10 year bond yield,
however for Japan we instead use the official discount rate. This is due largely to data
availability constraints and that the market for 10 year bonds (and similar maturities)
in Japan has not been liquid for most of the time period covered. We should note that
the discount rate is an official lending rate for banks in Japan, which implies it is
generally lower than a market rate.
Unlike many studies; see inter alia Mukherjee and Naka (1995) and Maysami
and Koh (2000); we do not include the exchange rate as an explanatory variable. We
reason the domestic economy should adjust to currency developments and thus reflect
the impact of foreign income due to firms’ exports measured in domestic currency
over the medium run. Additionally, in the white paper on the Japanese Economy in
1993, published by the Japanese Economic Planning Agency, it has been pointed out
that the boom in the economy during the late 1980s has been driven by domestic
demand rather than exports (Government of Japan, 1993).
In contrast to our study, many researchers have based their analysis on
business cycle variables or stock market valuation measures such as the term spread or
7
default spread for the former category or dividend yield or earnings yield for the latter.
Examples of those papers include Black, Fraser and MacDonald (1997); Campbell and
Hamao (1992); Chen, Roll and Ross (1986); Cochran, DeFina and Mills (1993); Fama
(1990); Fama and French (1989); Harvey, Solnik and Zhou (2002) and Schwert
(1990). These variables are usually found to be stationary and as we plan to model
long term equilibrium using non stationary variables we do not included them in our
model.
As McAdam (2003) has confirmed, the US economy has been characterized by
more frequent but less significant downturns relative to those suffered by the Japanese
economy. This might be explained by a higher capital and export orientated Japanese
economy relative to the US. We might therefore expect higher relative volatility in
corporate cash flows and hence also in Japanese share prices. A priori, therefore, share
prices in Japan may be more sensitive to changes in industrial production, although the
greater relative volatility may also influence the estimated coefficient standard errors
in any regression equation. However, previous research (see Binswanger, 2000) has
found that although both stock markets move positively with economic output, that the
coefficient for output on equity returns tends to be larger for the US data relative the
Japanese data. Campbell and Hamao (1992) also find smaller positive coefficients for
the dividend price ratio and the long-short interest rate spread on stock market returns
in Japan relative to the US in a sample covering monthly data from 1971 to 1990.
Thus the intuitive expectation of higher coefficients in Japan due to higher capital and
export exposure has not been confirmed empirically in existing research. Japan’s
banking crisis and subsequent asset deflation during the 1990s could have changed
significantly the influence of a number of variables, particularly the interest rate and
money supply.
8
To our knowledge, there has not been any empirical study of the present value
model in Japan after the early 1990s and thus the severe downturn with low economic
growth and deflation. Existing studies of the Japanese stock market before 1990
include Brown and Otsuki (1990), Elton and Gruber (1988), and Hamao (1988),
although these papers mainly consider stationary business cycle variables and risk
factors and therefore cannot give an indication of the empirical relationships we might
expect to find in our model.
In this paper we compare the US and Japan over the period January 1965 until
June 2005. The use of monthly data gives the opportunity to analyse a very rich data
set, to our knowledge earlier papers have only analysed shorter periods or have made
use of a lower data frequency. This allows us to include the impact of the historically
high volatility of both stock markets. The US stock market showed very high returns
between 1993 and 1999, while from 2000 until 2003 returns have been very large and
negative. In the Japanese stock market during the period from 1980 through to 1990,
returns have in the main been large and positive while they tend to have been large
negative for most of years between 1990 and 2003. The impact of recent problems to
the Japanese banking sector is also captured in our data (see Government of Japan,
1993). Most existing research has been applied to US data and very little is known
about the differences between US and Japanese stock market valuation. This paper
investigates the differences and common patterns in both countries in order to verify
whether the same variables that explain aggregate stock market movement in the US
can also be used to do so in Japan.
III. Empirical Methodology
As we are interested in modelling a long term relationship between macro
variables and the stock market, cointegration analysis is the ideal tool. We use the
9
Johansen (1991) procedure since it has been shown to have good finite sample
properties. The Johansen (1991) procedure is based on a vector error correction model
(VECM) to test for at least one long run relationship between the variables. For the
VECM we first determine the order of integration of the variables, making use of
Augmented Dickey-Fuller and the Phillips-Perron tests, and then apply the Johansen
procedure as follows: Consider a general Vector Autoregressive model with Gaussian
errors written in the following error correction form:
k −1
ΔX t = μ + ∑ Γi ΔX t −i +Π X t − k + φDt + ε t
(5)
i =1
Where εt is a sequence of zero-mean p-dimensional white noise vectors and Dt are
seasonal dummies. The term Xt includes our variables and is a p x 1 vector. The
parameters are the p x p matrix Γ and Π denotes a p x p matrix that contains the
information about the rank and hence the long term relationship among the variables.
There are three possible cases to be considered: Rank (Π) = p and therefore vector Xt
is stationary; Rank (Π) = 0 implying absence of any stationary long run relationship
among the variables of Xt or Rank (Π) < p and therefore r determines the number of
cointegrating relationships. The equation has an error correction representation where
Π =αβ’. The columns of matrix α are called adjustment (or loading) factors and the
rows of matrix β are the cointegrating vectors with β’xt being stationary even if Xt
consists individually of I(1) processes. Johansen developed two different tests of the
hypothesis that there are at most r cointegrating vectors; the trace statistic which tests
the null hypothesis of at most r cointegrating relationships against a general alternative
in a likelihood ratio framework and the maximum eigenvalue statistic which tests the
hypothesis of r cointegrating relationships against the defined alternative of r+1
cointegrating relationships.
10
IV. Empirical results
As a first step, unit root tests for the US and Japanese dataset have been applied to the
data. For brevity, we do not present the full results here 6 . We find all series to be I(1)
when we use the Phillips-Peron test and we proceed under the assumption that all
series (US and Japanese) have a unit root.
Our next step is to estimate the appropriate cointegrating vector using both the
US and Japanese data as follows:
US
SP500 = β1C + β2IP + β3CPI + β4M1 + β5 TB
(6)
Japan
NKY 225 = β1C + β2IP + β3CPI + β4M1 + β5Disco
(7)
Note that all series are in natural logarithms. SP500 is the real S&P 500 price, C
represents a constant term, IP is real Industrial Production, CPI is the consumer price
index, M1 represents real M1, the real ten year US T-Bond yield is given by TB, NKY
is the real Nikkei 225 and Disco is the real official discount rate (lending rate) in
Japan. For the US, Industrial Production, CPI and the ten year bond yield has been
taken from the IMF, M1 is taken from OECD while the S&P500 is downloaded from
Bloomberg. Japanese Industrial Production, CPI and the discount rate are taken from
the IMF, Japanese M1 and the Nikkei 225 are taken from the OECD and Datastream
respectively. Our data has a monthly frequency and our sample runs from January
1965 until June 2005. As industrial production, M1 and the CPI time series show
strong seasonality, seasonally adjusted data is used.
11
For the US data, the trace statistic suggests two, and the maximum eigenvalue
statistic one, cointegrating vector at the 5% significance level (see Table 1). Given the
evidence in favour of at least one cointegrating vector, we normalise the cointegrating
vector on the stock price and find a significantly positive coefficient on Industrial
Production, an insignificantly positive coefficient on M1 and a significantly negative
relationship between the stock price and both the 10 year T-Bond yield and CPI (Table
2). A test of the zero restriction confirms M1 does not have any explanatory power
and we re-estimate the cointegrating relationship without M1. One cointegrating
relationship is then confirmed for the four remaining variables and the signs of the
cointegration coefficients remain the same (Tables 3 and 4). Thus, the US stock
market shows a significantly positive relationship with industrial production, while
bond yields and CPI have a statistically significant negative relationship. The error
correction model shows that the S&P 500, the consumer price index as well as
industrial production contribute to the error correction process.
For the Japanese data, the trace statistic and the maximum eigenvalue statistic
test indicate two cointegrating vectors at the 10% significance level (see Table 5).
Thus we allowed for two cointegrating relationships in the Japanese data. We
normalised one cointegrating vector on the stock price and, as for the US data, found a
positive and significant relationship with industrial production, but in contrast to the
US results, a negative and significant relationship with the money supply.
Surprisingly, we found both the CPI and the discount rate to have an insignificant
influence over the stock price in this cointegrating vector. We normalised the second
cointegrating vector on industrial production and found a significantly negative
relationship with both the CPI and the discount rate (Table 6). 7
The results using US data are broadly in line with existing theory and evidence.
As expected and in common with most existing research (see inter alia Chen, Roll and
12
Ross, 1986, Cheung and Ng, 1998 and McMillan, 2001) we find a positive
relationship between industrial production and the stock price. In the case of CPI, the
US shows a negative coefficient for the stock price. This result is also supportive of
previous research (see inter alia Chen, Roll and Ross, 1986, Geske and Roll, 1983 and
Fama and Schwert, 1977). Also, as expected, and in common with previous research,
the US long-term interest rates show a negative influence on share prices. Finally, in
common with McMillan (2001), we find the money supply, M1, does not contribute
significantly to the stock price in the US. This perhaps suggests that the various
influences the money supply has on the stock price (discussed above) may ‘cancel’
each other out.
The interpretation of the Japanese results is a little less straightforward. For the
Japanese data there is also a positive relationship between industrial production and
the stock market, although the coefficient is higher, suggesting as discussed above, a
higher sensitivity of stock prices to industrial production.
However, when using the Japanese data, CPI is only significant in the second
cointegration vector, normalised on industrial production, where it yields a negative
relationship. Thus the influence of the CPI upon stock prices is negative only
indirectly, via the coefficient on industrial production. This finding is surprising and
differs from that of Mukherjee and Naka (1995), who find a negative coefficient on
CPI for a cointegrating vector normalised on the stock price. 8 One reason for this
difference may be due to the larger sample size in our study. Mukherjee and Naka
make use data from the period 1971 to 1990. This corresponds to a period of relatively
high inflation in Japan and stable (after the impact of the 1973 oil price shock) growth
in industrial production. Our sample includes the period of strong disinflation (in the
early 90s during the Japanese stock market downturn) and deflation in the late 90s and
early 21st century, falling stock prices and stagnant but volatile industrial production.
13
During periods of low inflation its impact upon stock prices, via unexpected inflation,
inflation uncertainty and a ‘Defina effect’ (as discussed above) is likely to be low. The
period of deflation and falling stock prices is also likely to reduce the magnitude of
any negative relationship over the rest of the sample.
The money supply M1 shows a significant negative coefficient on the
cointegration vector normalised on the stock price, when using the Japanese data. We
also find the coefficient, for the same vector, on the discount rate is insignificant. This
is an unexpected result that may also be at least partly due to the difficulties faced by
the Japanese economy since 1990 9 . Krugman (1998) has suggested the Japanese
economy has suffered from a Keynesian liquidity trap during the late 1990s and early
21st century (see also Weberpals, 1997 and also Svensson, 2003), and our findings
may be consistent with this. In particular our results are consistent with an increasing
money supply during the period (particularly after 1995) and falling interest rates that
were unable to pull the Japanese economy out of its slump, or prevent stock prices
from falling.
V. Conclusion
In order to achieve a deeper understanding of long term stock market
movements, a comparison of the US and Japanese stock market, using monthly data
over the last 40 years has been conducted. Using US data we found evidence of a
single cointegration vector between stock prices, industrial production, inflation and
the long interest rate. The coefficients from the cointegrating vector, normalised on the
stock price, suggested US stock prices were influenced, as expected, positively by
industrial production and negatively by inflation and the long interest rate. However,
we found the money supply had an insignificant influence over the stock price. In
Japan, we found two cointegrating vectors. One normalised on the stock price
14
provided evidence that stock prices are positively related to industrial production but
negatively related to the money supply. We also found that for our second vector,
normalised on industrial production, that industrial production was negatively related
to the interest rate and the rate of inflation. An explanation of the difference in
behaviour between the two stock markets may lie in Japan’s slump after 1990 and its
consequent liquidity trap of the late 1990s and early 21st century.
15
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Pesaran, M. H. and Timmermann, A., (2000), A Recursive Modelling Approach to
Predicting UK Stock Returns., Economic Journal, 110, 159-191
Posen, A., (2003), It takes more than a bubble to become Japan, Institute for
International Economics, Working Paper 03-9.
Rogalski, J.R. and J.D. Vinso, (1977), “Stock Returns, Money Supply and the
Direction of Causality”, Journal of Finance, 32, 1017-1030.
Ross, S.A., (1976), “The Arbitrage Theory of Capital Asset Pricing”, Journal of
Economic Theory, 13, 341-360.
Schwert, W., (1990), “Stock returns and real activity: a century of evidence”, Journal
of Finance, 45, 1237-1257.
18
Svensson, L. E. O., (2003), “Escaping from a Liquidity Trap and Deflation: The
Foolproof Way and Others”, Journal of Economic Perspectives, 17, 145-66.
Urich, T. and P. Wachtel (1981), “Market response to the weekly money supply
announcements in the 1970s”, Journal of Finance, 36, 1063-1072.
Weberpals, I., (1997), “The Liquidity Trap: Evidence from Japan”, Bank of Canada
Working Paper 97-4.
19
Table 1:
Sample US: 1965M06 2005M06
Trend assumption: Linear deterministic trend
Series: SP500 IP CPI M1 TB
Lags interval (in first differences): 1 to 12
Unrestricted Cointegration Rank Test (Trace)
Hypothesized
Eigenvalue
Trace
5%
No. of CE(s)
Statistic
Critical Value
None
0.0865
95.007 *
69.819
At most 1
0.0510
52.230 *
47.856
At most 2
0.0307
27.453
29.797
At most 3
0.0215
12.697
15.495
At most 4
0.0051
2.405
3.841
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized
Eigenvalue
Max-Eigen
5%
No. of CE(s)
Statistic
Critical Value
None
0.0865
42.777 *
33.877
At most 1
0.0510
24.778
27.584
At most 2
0.0307
14.755
21.132
At most 3
0.0215
10.292
14.265
At most 4
0.0051
2.405
3.841
p-value
0.0001
0.0183
0.0910
0.1264
0.1209
p-value
0.0034
0.1098
0.3064
0.1934
0.1209
Notes: Asterik denotes coefficient significance at 5% level, critical values are from
MacKinnon, Haug and Michelis (1999).
Table 2:
US Normalized cointegrating coefficients (standard error in
parentheses)
SP500
1.0000
00
IP
CPI
M1
TB
-2.475 *
(0.453)
[-5.467]
0.976 *
(0.264)
[ 3.704]
-0.267
(0.400)
[-0.670]
5.076
(2.556)
[ 1.986]
C
3.846
US Vector Error Correction with standard errors and t-values
ECM(1)
D(SP500)
D(IP)
D(CPI)
D(M1)
D(TB)
-0.049 *
(0.016)
[-3.029]
-0.007 *
(0.002)
[-2.979]
-3.0E-05*
(8.3E-05)
[-3.719]
8.82E-05
(0.002)
[ 0.046]
0.004 *
(0.001)
[ 3.242]
20
Table 3:
Sample US: 1965M06 2005M06
Trend assumption: Linear deterministic trend
Series: SP100 IP CPI M1 TB
Lags interval (in first differences): 1 to 12
Unrestricted Cointegration Rank Test (Trace)
Hypothesized
No. of CE(s)
None
At most 1
At most 2
At most 3
Eigenvalue
0.0924
0.0351
0.0128
0.0063
Trace
Statistic
71.815 *
25.976
9.088
2.989
5%
Critical Value
47.856
29.797
15.495
3.841
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized
Eigenvalue
Max-Eigen
5%
No. of CE(s)
Statistic
Critical Value
None
0.0924
45.839 *
27.584
At most 1
0.0351
16.888
21.132
At most 2
0.0128
6.099
14.265
At most 3
0.0063
2.989
3.841
p-value
0.0001
0.1294
0.3573
0.0838
p-value
0.0001
0.1774
0.6005
0.0838
Notes: Asterik denotes coefficient significance at 5% level.
Table 4:
US Normalized cointegrating coefficients (standard error in
parentheses)
SP55
IP
CPI
TB
1.000000
-2.445 *
0.938 *
6.216 *
(0.364)
(0.190)
(1.854)
[-6.711]
[ 4.945]
[ 3.353]
US Vector Error Correction with standard errors and t-values
D(SP500)
D(IP)
D(CPI)
ECM(-1)
-0.036 *
-0.007 *
-3.4E-04*
(0.015)
(0.002)
(7.7E-05)
[-2.356]
[-3.544]
[-4.414]
21
C
2.603
D(TB)
0.004 *
(0.001)
[ 3.323]
Table 5:
Sample Japan: 1965M01 2005M06
Trend assumption: Linear deterministic trend
Series: NKY225 IP CPI M1 Disco
Lags interval (in first differences): 1 to 12
Unrestricted Cointegration Rank Test (Trace)
Hypothesized
No. of CE(s)
None
At most 1
At most 2
At most 3
At most 4
Eigenvalue
Trace
Statistic
91.104 *
47.893 *
21.128
8.077
0.344
0.0873
0.0550
0.0272
0.0162
0.0007
5%
Critical Value
69.819
47.856
29.797
15.495
3.842
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized
Eigenvalue
Max-Eigen
5%
No. of CE(s)
Statistic
Critical Value
None
0.0873
43.211 *
33.879
At most 1
0.0550
26.764
27.584
At most 2
0.0272
13.051
21.132
At most 3
0.0162
7.733
14.265
At most 4
0.0007
0.344
3.841
p-value
0.0004
0.0496
0.3497
0.4572
0.5576
p-value
0.0029
0.0634
0.4475
0.4065
0.5576
Notes: Asterik denotes coefficient significance at 5% level.
Table 6:
Japan Normalized cointegrating coefficients (standard error in
parentheses)
NKY225
1.000
IP
-6.110 *
(0.556)
[-10.992]
CPI
0
M1
1.389 *
(0.291)
[ 4.780]
Disco
0
C
21.745
0
1.000
2.584 *
(0.399)
[ 6.482]
0
15.769 *
(5.131)
[ 3.073]
-21.194
Japan Vector Error Correction with standard errors and t-values
ECM(-1)
ECM(-2)
D(NKY225)
-0.015
(0.009)
[-1.728]
D(IP)
0.006 *
(0.002)
[ 3.332]
D(CPI)
-1.2E-04
(7.3E-05)
[-1.641]
D(M1)
-0.004 *
(0.001)
[-2.815]
D(Disco)
0.002
(0.001)
[ 1.536]
-0.021 *
(0.009)
[-2.361]
0.003
(0.002)
[ 1.689]
-6.94E-05
(7.6E-05)
[-0.911]
-0.00685 *
(0.00151)
[-4.531]
9.4E-04
(0.001)
[ 0.867]
22
1
Chen, Roll and Ross (1986) use a PVM framework to investigate the impact of systematic risk factors
upon stock returns, through factor influences on future cash flows or the discount rate of those cash
flows. They found that the yield spread between long and short term government bonds, expected
inflation, unexpected inflation, industrial production growth and the yield spread between corporate
high and low grade bonds significantly explain stock market returns.
2
In Japan the NIKKEI fell almost 75% over the 13 years from 1990.
3
The derivation of the PVM could easily be extended to allow a time-varying expected discount rate.
4
See inter alia Fama (1981), Chen, Roll and Ross (1986), Schwert (1990), Mukherjee and Naka
(1995), Cheung and Ng (1998) and Binswanger (2000)
5
For example see Chen, Roll and Ross, (1986)and Mukherjee and Naka, (1995)
6
Full unit root test results are available on request. Note we use the SIC criterion in order to determine
lag length in our tests.
7
These restrictions identify the two cointegrating vectors and are found to be binding using a Lagrange
Multiplier test. The relevant Chi-Square (2) test statistic is 0.079, which is insignificantly different from
zero
8
They also find two cointegrating vectors, although only report coefficients for the vector with the
highest eigenvalue.
9
For example, Mukerjee and Naka find a negative coefficient on the long term interest rate and a
positive coefficient on the the money supply for their cointegrating vector
23
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ABOUT THE CDMA
The Centre for Dynamic Macroeconomic Analysis was established by a direct grant from the
University of St Andrews in 2003. The Centre funds PhD students and facilitates a programme of
research centred on macroeconomic theory and policy. The Centre has research interests in areas such as:
characterising the key stylised facts of the business cycle; constructing theoretical models that can match
these business cycles; using theoretical models to understand the normative and positive aspects of the
macroeconomic policymakers' stabilisation problem, in both open and closed economies; understanding
the conduct of monetary/macroeconomic policy in the UK and other countries; analyzing the impact of
globalization and policy reform on the macroeconomy; and analyzing the impact of financial factors on
the long-run growth of the UK economy, from both an historical and a theoretical perspective. The
Centre also has interests in developing numerical techniques for analyzing dynamic stochastic general
equilibrium models. Its affiliated members are Faculty members at St Andrews and elsewhere with
interests in the broad area of dynamic macroeconomics. Its international Advisory Board comprises a
group of leading macroeconomists and, ex officio, the University's Principal.
Affiliated Members of the School
Dr Fabio Aricò.
Dr Arnab Bhattacharjee.
Dr Tatiana Damjanovic.
Dr Vladislav Damjanovic.
Prof George Evans.
Dr Gonzalo Forgue-Puccio.
Dr Laurence Lasselle.
Dr Peter Macmillan.
Prof Rod McCrorie.
Prof Kaushik Mitra.
Prof Charles Nolan (Director).
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Dr Ozge Senay.
Dr Gary Shea.
Prof Alan Sutherland.
Dr Kannika Thampanishvong.
Dr Christoph Thoenissen.
Dr Alex Trew.
Prof Joe Pearlman, London Metropolitan University.
Prof Neil Rankin, Warwick University.
Prof Lucio Sarno, Warwick University.
Prof Eric Schaling, Rand Afrikaans University.
Prof Peter N. Smith, York University.
Dr Frank Smets, European Central Bank.
Prof Robert Sollis, Newcastle University.
Prof Peter Tinsley, Birkbeck College, London.
Dr Mark Weder, University of Adelaide.
Research Associates
Mr Nikola Bokan.
Mr Farid Boumediene.
Mr Johannes Geissler.
Mr Michal Horvath.
Ms Elisa Newby.
Mr Ansgar Rannenberg.
Mr Qi Sun.
Advisory Board
Senior Research Fellow
Prof Andrew Hughes Hallett, Professor of Economics,
Vanderbilt University.
Research Affiliates
Prof Keith Blackburn, Manchester University.
Prof David Cobham, Heriot-Watt University.
Dr Luisa Corrado, Università degli Studi di Roma.
Prof Huw Dixon, Cardiff University.
Dr Anthony Garratt, Birkbeck College London.
Dr Sugata Ghosh, Brunel University.
Dr Aditya Goenka, Essex University.
Prof Campbell Leith, Glasgow University.
Dr Richard Mash, New College, Oxford.
Prof Patrick Minford, Cardiff Business School.
Dr Gulcin Ozkan, York University.
Prof Sumru Altug, Koç University.
Prof V V Chari, Minnesota University.
Prof John Driffill, Birkbeck College London.
Dr Sean Holly, Director of the Department of Applied
Economics, Cambridge University.
Prof Seppo Honkapohja, Cambridge University.
Dr Brian Lang, Principal of St Andrews University.
Prof Anton Muscatelli, Heriot-Watt University.
Prof Charles Nolan, St Andrews University.
Prof Peter Sinclair, Birmingham University and Bank of
England.
Prof Stephen J Turnovsky, Washington University.
Dr Martin Weale, CBE, Director of the National
Institute of Economic and Social Research.
Prof Michael Wickens, York University.
Prof Simon Wren-Lewis, Oxford University.
www.st-and.ac.uk/cdma
RECENT WORKING PAPERS FROM THE
CENTRE FOR DYNAMIC MACROECONOMIC ANALYSIS
Number
Title
Author(s)
CDMA06/09
Real Exchange Rate Volatility and Asset
Market Structure
Christoph Thoenissen (St Andrews)
CDMA06/10
Disinflation in an Open-Economy
Staggered-Wage DGE Model:
Exchange-Rate Pegging, Booms and the
Role of Preannouncement
John Fender (Birmingham) and Neil
Rankin (Warwick)
CDMA06/11
Relative Price Distortions and Inflation
Persistence
Tatiana Damjanovic (St Andrews)
and Charles Nolan (St Andrews)
CDMA06/12
Taking Personalities out of Monetary
Policy Decision Making?
Interactions, Heterogeneity and
Committee Decisions in the Bank of
England’s MPC
Arnab Bhattacharjee (St Andrews)
and Sean Holly (Cambridge)
CDMA07/01
Is There More than One Way to be EStable?
Joseph Pearlman (London
Metropolitan)
CDMA07/02
Endogenous Financial Development and Alex Trew (St Andrews)
Industrial Takeoff
CDMA07/03
Optimal Monetary and Fiscal Policy in
an Economy with Non-Ricardian Agents
Michal Horvath (St Andrews)
CDMA07/04
Investment Frictions and the Relative
Price of Investment Goods in an Open
Economy Model
Parantap Basu (Durham) and
Christoph Thoenissen (St Andrews)
CDMA07/05
Growth and Welfare Effects of
Stablizing Innovation Cycles
Marta Aloi (Nottingham) and
Laurence Lasselle (St Andrews)
CDMA07/06
Stability and Cycles in a Cobweb Model
with Heterogeneous Expectations
Laurence Lasselle (St Andrews),
Serge Svizzero (La Réunion) and
Clem Tisdell (Queensland)
CDMA07/07
The Suspension of Monetary Payments
as a Monetary Regime
Elisa Newby (St Andrews)
CDMA07/08
Macroeconomic Implications of Gold
Reserve Policy of the Bank of England
during the Eighteenth Century
Elisa Newby (St Andrews)
CDMA07/09
S,s Pricing in General Equilibrium
Models with Heterogeneous Sectors
Vladislav Damjanovic (St Andrews)
and Charles Nolan (St Andrews)
CDMA07/10
Optimal Sovereign Debt Write-downs
Sayantan Ghosal (Warwick) and
Kannika Thampanishvong (St
Andrews)
www.st-and.ac.uk/cdma
CDMA07/11
Bargaining, Moral Hazard and Sovereign
Debt Crisis
Syantan Ghosal (Warwick) and
Kannika Thampanishvong (St
Andrews)
CDMA07/12
Efficiency, Depth and Growth:
Quantitative Implications of Finance
and Growth Theory
Alex Trew (St Andrews)
CDMA07/13
Macroeconomic Conditions and
Business Exit: Determinants of Failures
and Acquisitions of UK Firms
Arnab Bhattacharjee (St Andrews),
Chris Higson (London Business
School), Sean Holly (Cambridge),
Paul Kattuman (Cambridge).
CDMA07/14
Regulation of Reserves and Interest
Rates in a Model of Bank Runs
Geethanjali Selvaretnam (St
Andrews).
CDMA07/15
Interest Rate Rules and Welfare in Open
Economies
Ozge Senay (St Andrews).
CDMA07/16
Arbitrage and Simple Financial Market
Efficiency during the South Sea Bubble:
A Comparative Study of the Royal
African and South Sea Companies
Subscription Share Issues
Gary S. Shea (St Andrews).
CDMA07/17
Anticipated Fiscal Policy and Adaptive
Learning
George Evans (Oregon and St
Andrews), Seppo Honkapohja
(Cambridge) and Kaushik Mitra (St
Andrews)
CDMA07/18
The Millennium Development Goals
and Sovereign Debt Write-downs
Sayantan Ghosal (Warwick),
Kannika Thampanishvong (St
Andrews)
CDMA07/19
Robust Learning Stability with
Operational Monetary Policy Rules
George Evans (Oregon and St
Andrews), Seppo Honkapohja
(Cambridge)
CDMA07/20
Can macroeconomic variables explain
long term stock market movements? A
comparison of the US and Japan
Andreas Humpe (St Andrews) and
Peter Macmillan (St Andrews)
For information or copies of working papers in this series, or to subscribe to email notification, contact:
Johannes Geissler
Castlecliffe, School of Economics and Finance
University of St Andrews
Fife, UK, KY16 9AL
Email: [email protected]; Phone: +44 (0)1334 462445; Fax: +44 (0)1334 462444.